First order linear differential equations

First order linear differential equations Quiz

Spec 4.2 · Edexcel International A Level Further Maths: Quiz

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  1. 1. Find the integrating factor for dydx+4y=x\frac{dy}{dx}+4y=x.

    • A. exe^{x}
    • B. 4x4x
    • C. e−4xe^{-4x}
    • D. e4xe^{4x}

  2. 2. Write xdydx+3y=x2x\frac{dy}{dx}+3y=x^2 in the form dydx+Py=Q\frac{dy}{dx}+Py=Q.

    • A. dydx+3xy=x\frac{dy}{dx}+\frac3xy=x
    • B. dydx+3y=x2\frac{dy}{dx}+3y=x^2
    • C. dydx+3xy=x2\frac{dy}{dx}+\frac3xy=x^2
    • D. dydx+3xy=x\frac{dy}{dx}+3xy=x

  3. 3. Find the integrating factor for dydx+2xy=…\frac{dy}{dx}+\frac2xy=\ldots for x>0x>0.

    • A. 2ln⁡x2\ln x
    • B. e2/xe^{2/x}
    • C. x2x^2
    • D. 1x2\frac{1}{x^2}

  4. 4. The equation dydx+ytan⁡x=…\frac{dy}{dx}+y\tan x=\ldots on 0<x<π20<x<\frac{\pi}{2} has integrating factor:

    • A. cos⁡x\cos x
    • B. sec⁡x\sec x
    • C. ln⁡sec⁡x\ln\sec x
    • D. sin⁡x\sin x

  5. 5. Solve dydx+y=e−x\frac{dy}{dx}+y=e^{-x}.

    • A. y=(x+C)exy=(x+C)e^{x}
    • B. y=Ce−x+xy=Ce^{-x}+x
    • C. y=xe−x+Cy=xe^{-x}+C
    • D. y=(x+C)e−xy=(x+C)e^{-x}

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